We report the results of J-band infrared spectroscopy of a sample of 13 z = 1 field galaxies drawn from the Canada-France Redshift Survey, targeting galaxies with redshifts that place the rest-frame Hα line emission from H II regions in between the bright night sky OH lines. As a result we detect emission down to a flux limit of ≃ 10-16 erg cm-2 s-1, corresponding to a luminosity limit of ≃1041 erg at this redshift for an H0 = 50 km s-1 Mpc-1, q0 = 0.5 cosmology. From these luminosities we derive estimates of the star formation rates in these galaxies that are independent of previous estimates based upon their rest-frame ultraviolet (2800 Å) luminosity. The mean star formation rate at z = 1, from this sample, is found to be at least three times as high as the ultraviolet estimates. The dust extinction in these galaxies is inferred to be moderate, for standard extinction laws, with a typical AV = 0.5-1.0 mag, comparable to that of local field galaxies. This suggests that the bulk of star formation is not heavily obscured, unless one uses greyer extinction laws. Star-forming galaxies have the bluest colours and a preponderance of disturbed/interacting morphologies. We also investigate the effects of particular star formation histories, in particular the role of bursts versus continuous star formation in changing the detailed distribution of ultraviolet to Hα emission. Generally we find that models dominated by short, overlapping, bursts at typically 0.2 Gyr intervals provide a better fit for the data than a constant rate of star formation. The star formation history of the Universe from Balmer lines is compiled and found to be typically 2-3 times higher than that inferred from the ultraviolet waveband at all redshifts. It cannot yet be clearly established whether the star formation rate falls off or remains constant at high redshift.